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111.
XU Chang-Zhi 《理论物理通讯》2006,46(3):403-406
Variable separation approach is introduced to solve the (2+1)-dimensional KdV equation. A series of variable separation solutions is derived with arbitrary functions in system. We present a new soliton excitation model (24). Based on this excitation, new soliton structures such as the multi-lump soliton and periodic soliton are revealed by selecting the arbitrary function appropriately. 相似文献
112.
Perturbation to symmetries and adiabatic invariants of a type of nonholonomic singular system 下载免费PDF全文
Based on the theory of symmetries and conserved quantities, the perturbation to the symmetries and adiabatic invariants of a type of nonholonomic singular system are discussed. Firstly, the concept of higher order adiabatic invariants of the system is proposed. Secondly, the conditions for existence of the exact invariants and adiabatic invariants are proved, and their forms are given. Thirdly, we study the inverse problems of the perturbation to symmetries of the system. An example is presented to illustrate these results. 相似文献
113.
FANHong-Yi 《理论物理通讯》2004,42(3):339-342
By virtue of the technique of integration within an ordered product of operators and the fundamental operator identity Hn(X)=2^n : X^n :, where X is the coordinate operator and Hn is the n-order Hermite polynomials,: : is the normal ordering symbol, we not only simplify the derivation of the main properties of Hermitc polynomials, but also directly derive some new operator identities regarding to Hn(X). Operation for transforming f(X) → : f(X) :is also discussed. 相似文献
114.
LIHui-Jun RUANHang-Yu 《理论物理通讯》2004,42(2):201-205
The inverse recursion operator, three new sets of symmetries, and infinite-dimensional Lie algebras for the nonlinear diffusion equation are given. Some nonlocal symmetries related to eigenvectors of the recursion operator with the eigenvalue λi are also obtained with the help of the recursion operator φi=φ-λi. Using a part of these symmetries we get twelve types of nontrivial new similarity reduction. 相似文献
115.
A new conserved quantity is deduced from Mei symmetry of Tzenoff equations for holonomic systems. The expression of this new conserved quantity is given, and the determining equation to induce this new conserved quantity is presented. The results exhibit that this new method is easier to find more conserved quantities than the previously reported ones. Finally, application of this new result is presented by a practical example. 相似文献
116.
Complex wave excitations general (2+1)-dimensional and chaotic patterns for a Korteweg-de Vries system 下载免费PDF全文
Starting from an improved mapping approach and a linear variable separation approach, a new family of exact solutions (including solitary wave solutions, periodic wave solutions and rational function solutions) with arbitrary functions for a general (2+1)-dimensional Korteweg de solutions, we obtain some novel dromion-lattice solitons, system Vries system (GKdV) is derived. According to the derived complex wave excitations and chaotic patterns for the GKdV 相似文献
117.
A Lattice Boltzmann Model and Simulation of KdV-Burgers
Equation 总被引:2,自引:0,他引:2
ZHANGChao-Ying TANHui-Li LIUMu-Ren KONGLing-Jiang 《理论物理通讯》2004,42(2):281-284
A lattice Boltzmann model of KdV-Burgers equation is derived by using the single-relaxation form of the lattice Boltzmann equation. With the present model, we simulate the traveling-wave solutions, the solitary-wave solutions, and the sock-wave solutions of KdV-Burgers equation, and calculate the decay factor and the wavelength of the sock-wave solution, which has exponential decay. The numerical results agree with the analytical solutions quite well. 相似文献
118.
Exact solutions of Kolmogorov-Petrovskii-Piskunov equation using the modified simple equation method
The modified simple equation method is employed to find the exact solutions of the nonlinear Kolmogorov-Petrovskii-Piskunov (KPP) equation. When certain parameters of the equations are chosen to be special values, the solitary wave solutions are derived from the exact solutions. It is shown that the modified simple equation method provides an effective and powerful mathematical tool for solving nonlinear evolution equations in mathematical physics. 相似文献
119.
Multiple positive solutions for superlinear second order singular boundary value problems with derivative dependence 总被引:1,自引:1,他引:0
闫宝强 《数学物理学报(B辑英文版)》2008,28(4):851-864
The existence of at least two positive solutions is presented for the singular second-order boundary value problem
{1/p(t)( p(t)x′(t))′+Φ(t)f(t,x(t),p(t)x′(t))=0,0〈t〈1,
limt→0 p(t)x′(t)=0,x(1)=0
by using the fixed point index, where f may be singular at x = 0 and px ′= 0. 相似文献
{1/p(t)( p(t)x′(t))′+Φ(t)f(t,x(t),p(t)x′(t))=0,0〈t〈1,
limt→0 p(t)x′(t)=0,x(1)=0
by using the fixed point index, where f may be singular at x = 0 and px ′= 0. 相似文献
120.
余家荣 《数学物理学报(B辑英文版)》2008,28(4):721-726
Some previous results on convergence of Taylor series in C^n [3] are improved by indicating outside the domain of convergence the points where the series diverges and simplifying some proofs. These results contain the Cauchy-Hadamard theorem in C. Some Cauchy integral formulas of a holomorphic function on a closed ball in C^n are constructed and the Taylor series expansion is deduced. 相似文献